• Students apply divisibility rules, specifically for 3 and 9, to understand factors and multiples.

Opening Exercise

Below is a list of numbers. Place each number in the circle(s) that is a factor of the number. You will place some numbers more than once.

Divisibility Rules

Divisibility rule for 2: If and only if its last digit is 0, 2, 4, 6, or 8.
Divisibility rule for 3: If the sum of the digits is divisible by 3.
Divisibility rule for 4: If and only if its last two digits are a number divisible by 4.
Divisibility rules for 5: If and only if its last digit is 0 or 5.
Divisibility rule for 8: If and only if its last three digits are a number divisible by 8.
Divisibility rule for 9: If the sum of the digits is divisible by 9.
Divisibility rule for 10: If and only if its last digit is 0.

Example 1

Is 378 divisible by 3 or 9? Why or why not?

a. What are the three digits in the number 378?
b. What is the sum of the three digits?
c. Is 18 divisible by 9?
d. Is the entire number 378 divisible by 9? Why or why not?
e. Is the number 378 divisible by 3? Why or why not?

Example 2

Is 3,822 divisible by 3 or 9? Why or why not?

Exercises

Circle ALL the numbers that are factors of the given number. Complete any necessary work in the space provided.

Lesson Summary

To determine if a number is divisible by 3 or 9:

Calculate the sum of the digits.

If the sum of the digits is divisible by 3, the entire number is divisible by 3.

If the sum of the digits is divisible by 9, the entire number is divisible by 9.

Note: If a number is divisible by 9, the number is also divisible by 3.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.